Molecular Dynamics Study of the Conformational Properties ...
Transcript of Molecular Dynamics Study of the Conformational Properties ...
James Gayvert1, Alexandros Chremos2, Jack Douglas2
1Le Moyne College, 2National Institute of Standards and Technology(NIST), U.S. Department of Commerce, Gaithersburg, Maryland, USA
Molecular Dynamics Study of the Conformational Properties of Polymers
in an Explicit Solvent and the Identification of the θ-Temperature
POLYMERS
Large molecule/macromolecule composed of repeating subunits called monomers
Polystyrene(Styrofoam) Polyisoprene(rubber) Insulin Hexamer DNA
Image from:
https://www.theodysseyonline.com/ne
w-year-no-more-styrofoam
Image from:
https://www.tirerack.com/content/t
irerack/desktop/en/homepage.html
Image from:
https://en.wikipedia.org/
wiki/Insulin
Image from:
http://exchange.smarttech.com/search.
html?q=%22DNA%20structure%22
POLYMER MODELS
o Ideal Chain:
o Modeled after a random walk model (no
attractions, no repulsions)
o “Real Chain”:
o Incorporates interactions between all
segments
o Includes a repulsive excluded volume
interaction and an attractive
component that allows us to account
for the quality of the solvent
A typical ideal chain
https://en.wikipedia.org/wiki/Ideal_chain
FLORY THEORY/SCALING LAW
𝑅𝑔~𝑁𝜈 𝑅𝑔
2 =1
𝑁σ𝑘=1𝑛 𝑟𝑘 − 𝑟𝑚𝑒𝑎𝑛
2
Rg is the radius of gyration of the polymer For a good solvent, ν≈3/5
N is the degree of polymerization(# of segments) For the θ-solvent, ν ≈ 1/2
𝜈 Is the Flory exponent For a poor solvent, ν ≈ 1/3
Solvent quality depends on chemistry and temperature
SOLVENT QUALITY
• “Good solvent”:• Monomers prefer to interact
with the solvent particles rather
than with other monomers
• Repulsive interactions dominate
• Polymer swells
• “θ-solvent”:• Attractive and repulsive
interactions are equal
• Polymer behaves as if it’s an
ideal chain
• “Poor solvent”• Monomers prefer to interact
with other monomers rather
than with solvent particles
• Attractive forces dominate
• Polymer contracts and behaves
more as a hard sphere
Images from: http://rkt.chem.ox.ac.uk/lectures/pol.html
OBJECTIVES
• Develop a model that can identify the θ-temperature
of a polymer solution
• Use molecular dynamics to simulate polymers of
varying chemistries and molecular architectures in an
explicit solvent
MOLECULAR DYNAMICS SIMULATIONS
Set initial conditions, particle
positions/velocities, and select
ensemble (NPT,NVE etc.)
Calculate forces from particle
positions using chosen
interaction model
Solve Newton’s equations of
motion(integrate)
Write Data to Disk/Analyze
Results
Loop over
time-steps
Animation from
https://en.wikipedia.org/wi
ki/Molecular_dynamics
IMPLICIT SOLVATION WORK• Implicit solvation work on this topic has been done by Steinhauser M.O. In J. Chem. Phys. 122(2005) on flexible linear polymer chains of
varying molecular masses
• Used a coarse grained bead-spring model that introduced a dimensionless parameter 𝜆 which determines the depth of the intermolecular potential
• Larger 𝜆=greater attractive forces between segments
• The overall intermolecular potential has the form
𝑉𝑖𝑛𝑡𝑒𝑟 𝑟 = ൞𝑉𝑊𝐶𝐴 𝑟 − 𝜆𝜖, 0 < 𝑟 < 21/6𝜎
𝜆𝑉𝑐𝑜𝑠 𝑟 , 21/6 ≤ 𝑟 < 𝑟𝑐𝑢𝑡0 𝑒𝑙𝑠𝑒
𝑉𝑊𝐶𝐴 𝑟 = 4𝜖𝜎
𝑟
12
−𝜎
𝑟
6
+ 𝜖
𝑉𝑐𝑜𝑠 𝑟 =1
2cos 𝛼𝑟2 + 𝛽 + 0.5 𝜖
Where 𝛼 and 𝛽 are parameters that fit the
cosine curve to smoothly approach 0 at the cutoff
Image from:
Steinhauser M.O
Int. J. Mol.
Sci. 2009, 10(12)
Steinhauser M.O. J.
Chem. Phys
122(2005)
𝜆=0 purely
repulsive
interactions
IMPLICIT SOLVATION WORK
Image from: Steinhauser M.O Int. J. Mol. Sci. 2009, 10(12) Steinhauser M.O. J. Chem. Phys 122(2005)
θ-temperature
𝝀 ≈ 𝟎. 𝟔𝟓
WHY USE AN EXPLICIT SOLVENT?
Explicit Solvent Implicit Solvent• Provides a more realistic and
detailed full-atom description of
the system
• Essential to reproduce certain
properties of solute molecules
• Reaction kinetics
• Dynamics
• Computationally expensive…
but worth it
Image from: http://csb.stanford.edu/~koehl/ProShape/born.php
SIMULATION DETAILS• Used a coarse grained bead model with an explicit solvent to try and
determine the 𝜃-temperature of various polymers of different molecular
architectures and chemistries
• NPT Ensemble
• The Lennard Jones Potential was used with a cutoff of 2.5σ
• Used ZENO numerical path integration software to obtain conformational
properties of the generated polymer chains (radius of gyration,
hydrodynamic radius, etc)
𝑉𝐿𝐽 𝑟 = 4𝜖𝜎
𝑟
12
−𝜎
𝑟
6
Image from: http://www.sklogwiki.org/SklogWiki/index.php/Lennard-Jones_model72000 solvent particles + polymerPolymer chain with 41 monomers
SYSTEMS STUDIED
Linear Chain Ring Polymer
Molecular Mass: 41,81,161,321
Temperature=0.5,0.7,0.9
εpp for polymer-polymer interactions: 1.0
εss for solvent-solvent interactions: 1.0
εsp cross interactions: Modified Lorentz Berthelot
mixing rule
εsp = ε𝑝𝑝 ∗ ε𝑠𝑠 1 − 𝛼
𝛼=.0, 𝛼=.02, 𝛼=.04, 𝛼=.06, 𝛼=.08, 𝛼=.1, 𝛼=.12, 𝛼=.14, 𝛼=.16,
WHAT SHOULD OUR MIXING RULE BE?
𝛼 ≥ 0.06Collapsed Region
Always poor solvent
conditions
𝛼=0
Swollen Region
Good solvent
conditions
0.02<𝛼<0.04
Intermediate Region
Rg is sensitive to
changes in temperature
SWOLLEN REGION-LINEAR
• 𝛼=0
• No clear trend between <Rg> and
temperature, difficult to identify
𝜃-temperature
• Chains are more swollen, cross
interactions too attractive (good
solvent conditions)
• Cannot naively choose mixing rule
𝛼 ≥ 0.06Collapsed Region
Always poor solvent
conditions
𝛼=0
Swollen Region
Good solvent
conditions
0.02<𝛼<0.04
Intermediate Region
<Rg> is sensitive to
changes in temperature
COLLAPSED REGION-LINEAR
• 𝛼 ≥ 0.06• Chain is always collapsed, cross
interactions too repulsive (bad
solvent conditions)
• Desired behavior was not achieved
for these simulations, no crossover
occurs
𝛼 ≥ 0.06Collapsed Region
Always poor solvent
conditions
𝛼=0
Swollen Region
Good solvent
conditions
0.02<𝛼<0.04
Intermediate Region
Rg is sensitive to
changes in temperature
FUTURE WORK
• Increase resolution of search for 𝜃-temperature
• Explore 0 < 𝛼 < 0.06
• Explore more temperatures within range
0.5<T<0.9
• Explore different types of molecular architectures
• Find 𝜃-temperature for branched polymers
Branched/Star Polymer